Constant field strengths on T^{2n}

TL;DR

This paper investigates constant diagonal field strength configurations in U(N) Yang-Mills theory on 2n-dimensional tori, deriving fluctuation spectra and eigenfunctions, with implications for higher-dimensional D-branes and string theory.

Contribution

It extends Van Baal's work on T^4 to higher dimensions, providing explicit eigenfunctions and analyzing fluctuation spectra in these configurations.

Findings

Eigenfunctions expressed via theta functions on tori

Spectrum of fluctuations explicitly determined

Relevance to higher-dimensional D-branes and string theory

Abstract

We analyse field strength configurations in U(N) Yang-Mills theory on T^{2n} that are diagonal and constant, extending early work of Van Baal on T^4. The spectrum of fluctuations is determined and the eigenfunctions are given explicitly in terms of theta functions on tori. We show the relevance of the analysis to higher dimensional D-branes and discuss applications of the results in string theory.